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Chapter 2: Q.48 (page 62)

You are driving to the grocery store at 20 m/s. You are 110 m

from an intersection when the traffic light turns red. Assume

that your reaction time is 0.50 s and that your car brakes with

constant acceleration. What magnitude braking acceleration will bring you to a stop exactly at the intersection?

Short Answer

Expert verified

The magnitude of acceleration which brings the person to stop exactly at intersection is2m/s2.

Step by step solution

01

Given data

The speed of the person while moving towards grocery shop, v=20m/s.

The reaction time of the person is, t=0.5s

The distance of intersection from the starting position of the car is, D=110m

Consider the person applied the brake which is at ddistance from the starting position

02

Determination of the distance d

According to the question, the distance travelled by the person at a constant speed v=20m/sis,

x=vtx=20×0.5mx=10m

So the person strike the brake at a distance of,

d=D-xd=110-10md=100m

03

Determination of acceleration

The acceleration at the point of intersection can be determined by the equation asv02=v2+2ad.

Therefore,

role="math" localid="1648566235908" v02=v2+2ad0=202+2a×100a=0-202200a=-2m/s2

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